Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×S5 |
| unambiguous semidirect product | A5⋊(C2×C9) |
| derived | A5 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C9 | S5 |
| commutator, hypocenter | A5 | C2×C9 |
| Frattini | C3 | C3×S5 |
| socle, cosocle | C3×A5 | C2×C3 |
| prime radical | C3×S5 | C3 |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C9 | |
63 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 45 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 261);